I’ve watched some Anime films and really enjoyed them and I’d appreciate it if people could recommend some more that are worth watching.
I’ve seen:
Appleseed and Appleseed: Ex Machina
The Ghost in the Shell films and the two GITS: SAC series
Macross Plus
Akira
Thanks!
Anime has a lot of different subgenres and what you’ll like depends tremendously on your particular taste. I can recommend a few of my favorites but I haven’t seen any of the stuff you have so I can’t really tell how much you might agree.
One recommendation I make to everybody:
Paranoia Agent: This is a fairly atypical anime and I consider it hands-down the most worthwhile show I’ve seen. It starts out fairly weird and gets weirder, but it’s short and it will all make sense once you finish it. Just from what I’ve heard about GITS if you liked that I suspect this will be your kind of thing as well.
My other favorites:
The Melancholy of Suzumiya Haruhi: A more standard anime high school hijinks sort of show but simply a cut or three above the rest. This is my second favorite show, being funny, clever, and amazingly well-made. I know some people weren’t as charmed with it as I was, but those that I know who do like it all like it a lot. Be sure you watch the episodes in the order they aired on TV, the North American DVD release for some unfathomable reason changed it.
Ouran High School Host Club: This is another of my favorite shows, and a lot of the reasons I like it are in common with Haruhi. Where Haruhi is a spectacular affectionate parody of standard school romance anime, Ouran is its counterpart for shoujo (shows aimed at girls). Make no mistake, though, if you skip this show because it’s “girly” then you’re missing out.
Some more YMMVish recommendations:
Kare Kano (full title Kareshi Kanojo no Jijou): I loved this show, but among people I know it seems very polarizing. Just as an attempt to extrapolate from my limited sample, it seems more likely you’ll like this if you have an appreciation for sarcastic humor, if you’re at least a little vain or arrogant (certainly a character flaw of mine), and can appreciate well-done romance comedy (vanishingly rare in the genre by that name here in the US imo). If you don’t like the first two or three episodes, bail out. And just as a heads-up, this show had some crises in development and the second half of the show is comparatively weak.
Full Metal Panic: This is one of my favorite shows but objectively I can’t claim it’s as good as some of my more recommended ones, it’s just one I have a soft spot for. The real star here is the second season, titled Full Metal Panic: The Second Raid. The first season of FMP was by the animation studio Gonzo, and was a decent but unspectacular effort. After the humorous-short-story intermediate season was handed to Kyoto Animation instead, apparently Kyoto’s work was considered so much better that they were commissioned to do the sequel series. In my opinion this second season turned FMP from a promising but somewhat lackluster show into a great one. This is a combined school romance and comedy and mecha show played straight, and it’s my favorite of them.
Full Metal Alchemist: despite the name this and FMP are totally unrelated. This was the show that really got me watching anime. I think what impressed me the most, especially in contrast to TV here, was that this show told a story. Everything that happened happened for a reason, with remarkably little filler and while managing to be fun and interesting all along the way. I feel I may view this show to an extent through rose-colored glasses because it was one of the first anime I watched. A lot of what I liked about it includes many of the ways anime as a whole tends to differ from American television, but this show is also widely known for its quality and is quite popular.
Rurouni Kenshin: Tsuiokuhen (or Samurai X: Trust and Betrayal): This is the movie, not the TV series titled Rurouni Kenshin (which I have not heard good things about). As a movie, it doesn’t take much of an investment to watch and is routinely praised as one of the best creations of anime. It’s a samurai story and is quite violent, but if that doesn’t bother you then you should check it out.
Mushishi: Along with Samurai X: T&B, this show ignores standard anime tropes and does its own thing. This is a 26 episode show that is more like a collection of short stories. It tends to be rather slow and contemplative, but if you like well-done stories even of the more thoughtful rather than action-packed variety then this is more than worth a look.
Quick list of other shows I liked but not quite as much as the above:
Welcome to the NHK (could join the above when I finish it)
Higurashi no Naku Koro ni (if you don’t like excessive violence then STAY AWAY)
Elfen Lied (see note on Higurashi)
Fruits Basket
Lucky Star
Tengen Toppa Gurren Lagann
Death Note
Kanon
Cardcaptor Sakura
Mai-Hime
Monster
Anything by Hayao Miyazaki, but in particular:
Princess Mononoke
Spirited Away
Nausicaa and the Valley of the Wind
Howl’s Moving Castle
I’m not a huge anime fan as a rule, but these four are among the best movies ever made.
That’s a pretty good assessment.
Hey, I’ve got some of the above on my viewing list, too.
Just now, I finished watching Samurai Champloo and want to put in a good word for it. It’s by the creator of Cowboy Bebop (which I haven’t seen, to be honest), and it’s a quirky and fun take on the Samurai action genre.
Not all the episodes have the same quality story-telling wise, and the quality of animation drops after the first episode, but the episodes that move the main plot ahead are great.
This makes me curious, as Kenshin was one of the hugely popular anime of the 90’s. I recommend it, the characters are a lot of fun. It ran for 92 episodes, so certainly SOME people loved it!
A lot of my recommendations are a bit older, as I was mostly big into the anime fandom during high school and that was 10 years ago. Back when we had to rely on fansubbers to translate titles and everything was on VHS.
I do recommend the films of Satoshi Kon, particularly Perfect Blue. It’s an intense psychological horror type of movie where at the end you have no idea if the character is completely insane or truly victimized. The more recent Millennium Actress is a great story about a woman searching for her love through various roles/lives. Kon likes the surreal and the symbolic, so both films deserve a couple viewings to see some of the smaller, more subtle symbols he likes incorporate.
Revolutionary Girl Utena is my personal favorite series ever. It takes a lot of the typical shoujo tropes (magical girls, sexy, ambigously gendered bishounen, princesses and animal sidekicks) and utilizes them, while at the same time twisting the genre a bit to include strange, postmodern symbology. The basic story is a young girl at a prestigious academy who gets pulled into a secret club of students who duel for posession of another student, who is called the Rose Bride. Utena, the main character, ends up winning the girl and decides to continue fighting to free her from the cycle of the crazy duels. The culmination is a great study of what it means to be truly noble and the sacrifices that can change a Prince to a Devil.
I re-watch this show often.
A newer show that I was really impressed with is Ergo Proxy. It’s deeply referential of philosophy and philosophers, and a great post-apocalyptic story about AI. Great science fiction and really great animation.
Wolf’s Rain is another new one that I enjoyed, another postapocalyptic story in which wolves are thought to be extinct but instead walk among humans while hiding behind a kind of glamour that makes them seem human. The four main wolves are searching for a fabled paradise in which they can live in the wild again.
Let’s see, other shows that are a lot of fun are:
Sorcerer Hunters (pervert, his prude brother, and two S&M sisters hunt evil sorcerers, hijinks ensue)
Excel Saga (completely absurd)
**Fushigi Yuugi **(Girl gets sucked into ancient China; very girly, if you’re not into shoujo)
**Record of Lodoss War **(the OVAs are the best, very good medieval swords and sorcery tale, a classic)
Vision of Escaflowne (mecha meets medieval, very good)
And if you haven’t, **Mononoke Hime **(Princess Mononoke) is a must see for pretty much everyone, everywhere.
If it’s anime you want, you need to see Metropolis. Hands-down my all time favorite; it’s got a dark and siniste plot juxtaposed with the innocence of childhood friends, and a killer jazz soundtrack. Really, go watch it now.
Oh, and I second pretty much everything the others said. (We are the coolest. Geeks. Evar! 
)
I like Royal Space Force: The Wings of Honneamise and can’t say enough good things about Cowboy Bebop.
I’ll second the recommendations for The Melancholy of Suzumiya Haruhi, Full Metal Panic, Fullmetal Alchemist and Samurai Champloo.
Ouran High School Host Club is good, but watching it with the wrong people can really ruin the experience: I don’t know if you know anyone of the “screaming fangirl” type, but their reactions during this series will make you want to throttle them.
I didn’t like Howl’s Moving Castle or Wolf’s Rain. I quickly became indifferent to some of the major characters of the first, and didn’t get past the first episode of the other.
Others:
Death Note is a series about a high school student who is trying to set himself up as a god of vengeance. I do recommend it, although I haven’t finished watching it yet.
Tengen Toppa Gurren Lagann is basically mecha action powered by awesome. It’s silly and over the top, but good fun to watch, from what I’ve seen.
Last Exile is a series set in a world with flying capital ships and smaller two-person “vanships”. The protagonists are a pair of couriers who fly one of these vanships.
You know, Death Note sounds incredibly bad when you forget to mention the part about the actual Death Note, I mean what you said is technically true but… 
Anyway a lot of good ones mentioned, a few that haven’t been touched on:
I’ve heard good things about Geobreeders and Samurai Girl: Real Bout High School, I’ve only seen one episode of each. The first was pretty cool, the second was not in my taste, but I could see myself watching it with nothing else to do.
Vampire Hunter D was pretty much made for Western Audiences (much like Cowboy Bebop was, though the series aren’t compatible at all), wasn’t my favorite, it’s a C+, the OVA was okay though.
FLCL/Fooly Cooly: They spent 24 episodes worth of production budget on 6 episodes. It’s very well done, but is incredibly confusing. You may have to watch it a few times. My friend and I are currently on a bet about whether we understand it because there really is an allegory or if it just fucked up our brains to think in FLCL logic. This is possibly one of, in not my favorite anime.
Neon Genesis Evangelion: Not the absolute best, but considered a “must, even if you hate it” by some people. It falls apart into incomprehensibility in the last few episodes, even after you watch the movies it can be crazy. One of the rules of the universe is “we do NOT, under any circumstances, discuss the ending of NGE.”
Serial Experiment: Lain - It’s love or hate, I like it, but it’s even more confusing that Neon Genesis Evangelion and FLCL, I’m pretty sure if you bred the production teams of NGE, FLCL, and SE:L (and maybe Haruhi Suzumiya) and had those children produce an anime the universe would explode. This anime doesn’t have episodes, it has layers. And wikipedia can’t even come up with a plot, it has theories about the plot, because there isn’t actually any fan agreed upon plot that I’m aware of.
One of the .hacks. Not sure which one it was, I think it was an OVA. In this one there was actually an epidemic for people who were playing the game (The World) randomly passing out and getting stuck. The main character was female. This is the only .hack I actually like (sorry guys, I’ll turn in my badge //sign was boring as hell, no dialogue, no action, just… scenery. It felt like it at least Music was good though) I think it’s .hack//Limnality I’m thinking of, but I’m not sure.
Märchen Awakens Romance (Mär Heaven). I love this anime. The English Dub died really fast, but I found it to be a really well done show, then again I have no taste.
G Gundam is good, and was the first anime I really watched knowing what anime was (as opposed to “that show on Cartoon Network” like, say Tenchi or Sailor Moon, which i still hold dear to me). It’s good, but pretty cheesy when I tried to watch it again. It’s not the best animated thing ever, but I (gasp another badge revoked) like it more than Mobile Suit, SEED and whatnot.
Berserk and Claymore have droves of fanbois, they’re good if you like Dark Fantasy, if you don’t… run away.
There’s also the obvious ones everyone knows about (Naruto, Dragonball, Sailor Moon, Cardcaptor etc) even if they’re not into Anime, but I’ll leave whether they want to see them or not as an exercise to the reader.
For the finest in Japanese Ultraviolence, what has been termed “the pronographt of violence”, I strongly recommend Black Lagoon.
Tarantino wishes he could cream this much mayhem into a flick.
The following, mentioned upthread, I give a very strong “seconded!”:
Spirited Away - a must see. Cinema doesn’t get much better than this
Princess Monokoke
Perfect Blue - one of the best psychological thrillers I’ve ever seen, and not just in anime
Millenium Actress - fantastic storytelling, and the art is first-rate
Not mentioned yet, that I highly recommend:
Cowboy Bebop - ran for one single season, and there’s also a movie that was made afterward (that’s supposed to take place towards the later part of the season, chronologically). It’s a sci-fi with wild west sensibilities (sorta like Firefly). Follow a small crew of bounty hunters as they travel the galaxy trying to make an honest living, hoping their shady pasts don’t catch up with them. It’s got one of the best soundtracks ever written, incredibly deep characters, and a lot of wit in the storytelling. This is one of my favorites, and one I always use to expose non-anime watchers to the genre, always to good effect.
Jin-Roh: The Wolf Brigade - Directed and scripted by the same folks who brought you Ghost in the Shell, this futuristic dystopia explores the life of a special unit agent who has doubts about the totalitarian government he is serving. As his conscience begins to rebel, he finds himself targeted by very powerful men, and the conspiracies around him deepen as he becomes haunted by the face of a girl he had a hand in killing, all the while being “reprogrammed” by his handlers. I have a suspicion that the “Fallout” series of computer games borrowed a lot of art design from this movie, particularly for the Enclave.
Grave of the Fireflies - follows the lives of two orphaned siblings in the aftermath of WWII. I have a difficult time with this one - it is simultaneously heartwrenching and inspiring, and is one of the most beautiful war/post-war movies I’ve ever experienced. It tends to wreck my night though, so if I’m going to watch it, I save it until right before bedtime. I consider this one a must-see, as well.
Vampire Hunter D - the original one, though the sequel is pretty decent, too. It’s a classic monster-hunter movie, and the animation is a little dated by today’s standards, but it’s incredibly atmospheric and deeply layered with gothic horror. Plus, the title character just kicks all sorts of ass.
Since the biggies have been mentioned…
Death Note and Jin-Roh are the best of the series and standalones, respectively. Death Note’s premise is silly at first glance. Give it a shot anyway.
Claymore is very good in most regards but utterly fails towards the end. Berserk is the polar opposite, mediocre animation atop a flimsier story - but becomes fleshed out through its conclusion, and is ultimately the better series of the two.
Elfen Lied is a strange Japanese variation of Stephen King’s “Carrie.” If nothing else, listen to the beautiful intro theme. http://www.youtube.com/watch?v=3EoCGwHz3T0
I heartily recommend Cowboy Bebop. It’s the only series I would feel comfortable recommending to even non anime fans.
Hard to beat Trigun for me. Just deep enough - not overly deep to the point of being convoluted, pretentious, or confusing like a lot of anime. Just funny enough. And the main character is just badass enough. It’s the perfect recipe. One of the best things I’ve ever seen - anime or not.
Some more not mentioned already:
My Neighbor Totoro – About two girls moving to a new house with their father to be closer to their mother, who is sick in hospital, and their interaction with the semi-divine Totoro.
Kamichu! – About a middle school girl who has just become a god, but continues to combine her divinity with just being an ordinary shy girl. A lot like Totoro, in showing a slice of ordinary Japanese life mixed in with the kami (spirits/gods) that hang around everywhere.
Figure 17: Tsubasa & Hikaru – Another series about a pre-teen girl, who lives with her baker father in Hokkaido, and suddenly acquires a twin sister (where the twin comes from is explained at the start: Tsubasa knows where Hikaru came from, but her father and the neighbours don’t). About 10% sci-fi monster fighting, and 90% every day life in countryside Hokkaido – and Tsubasa becoming a happier person with her new sister.
Sayonara Zetsubō Sensei – Completely different from the first three here, a brilliant parody with a teacher and his class full of extreme prototypical students. The teacher tries to kill himself in every episode from despair, and is helped each time by the insanely cheerful student Kafuka (= Franz Kafka). Full of the most brilliantly witty jokes.
Zipang – Another completely different genre. A late 20th century Japanese naval vessel gets sent back 60 years to the Battle of Midway, then spends the rest of the series trying not to change history, while surviving in an ocean where both the US navy and the Imperial Japanese Navy are hostile.
I’ve watched three or four fansubbed episodes of that. Between the subtitles and listening to the Japanese I can actually get most of what’s going on. Just listening to the Japanese, hell no. It’s way too fast; like listening to a New York-born reincarnation of Robin Williams when he was doing serious coke. There are also tons of background notes, signs, and other things that are important to getting some of the jokes.
It helps IMMENSELY to both understand Japanese language and culture, as well as anime conventions. They do their best to turn those conventions inside out, lampoon cultural stereotypes, and just plain screw with your head. It’s more random than the already extremely random anime norm. Very fun, but definitely not beginner viewing. Heck, the only reason I appreciate it, since I’m not the biggest anime fan out there, is because I’ve been steeped in the culture for several years and get some of the stuff through osmosis.
I like the more serious and quiet anime best, ones that don’t have many genre-specific conventions. In other words, movies that could easily have been done in a different form and been just as well received. Directors like Mamoru Oshii (Ghost in the Shell, Innocence, Jin-Roh) and Miyazaki Hayao (Princess Mononoke, Spirited Away) or series like the original Gundam and Macross. Satoshi Kon, who did Perfect Blue and Paprika, is also a darn good director, though he isn’t prolific. I’ve only seen a few episodes of Cowboy Bebop, but I thought it was pretty good, and as accessible as any non-anime SF.
I was exaggerating of course. 
Yeah understanding the culture makes it easier, but even so most people don’t understand the underlying allegory the first time through.
Naota, yeah? That horn? Um… horn yeah, it’s a coming of age story about puberty. And I’m not saying that to be juvenile either, there’s a pretty obvious correlation between something “hot” happening and the horns.
And it’s not all Japanese pop culture they spoof a bit of American as well, South Park in episode 5 springs to mind.
Ledgend of the Overfeind, Ninja reserection, Ninja Scroll, Crying Freeman, Wicked city, Devilman, The Guyver, Fatal Fury, Bleach, And AfroSamurai( by the same as people as Samurai Champloo, and stars Samuel Jackson{now thats whao(.%)}) And This one is way too Kool for school so if you’re luck enough to find it try not to tell too many, but its gonna be hard "Jo-Jo’s Bizare Adventures Enjoy all.
Thanks everyone! Lots to work through there…